10개의 극점이 각 주위에 씩 떨어져 반지름 r=0.9 주위에 모여 있는 IIR필터를 고려할 때, 크기 응답을 계산하고, 그려보자.

ex6_27.cem

r = 0.9; theta = (pi/180)*[-55:-35:5, 35:55:5]';
p = r*exp(j*theta); a = poly(p); b = 1;
w = [0:500]*pi/500; H = freqz(b*1e-4,a,w);
magH = abs(H); magHdb = 20*log10(magH);
 
% Direct form: quantized coefficients
N = 15; [ahat, L, B] = Qcoeff(a,N);
TITLE = sprintf("%i-bit (1+%i+%i) Precision (DF)", N+1, L, B);
Hhat = freqz(b*1e-4, ahat, w); magHhat = abs(Hhat);
 
% Cascade form: quantized coefficients: Same N
[b0, B0, A0] = drt2cas(b,a); [BAhat1,L1,B1] = QCoeff([B0,A0], N);
TITLE1 = sprintf("%i-bit (1+%i+%i) Precision (CF)", N+1, L1, B1);
Bhat1 = BAhat1(:,1:3); Ahat1 = BAhat1(:, 4:6);
[bhat1,ahat1] = cas2dir(b0,Bhat1,Ahat1);
Hhat1 = freqz(b*1e-4,ahat1,w); magHhat1 = abs(Hhat1);
 
% Cascade form: quantized coefficients: Same B (N = L1 + B)
N1 = L1+B; [BAhat2,L2,B2] = QCoeff([B0,A0], N1);
TITLE2 = sprintf("%i-bit (1+%i+%i) Precision (CF)", N1+1, L2, B2);
Bhat2 = BAhat2(:,1:3); Ahat2 = BAhat2(:, 4:6);
[bhat2,ahat2] = cas2dir(b0,Bhat2,Ahat2);
Hhat2 = freqz(b*1e-4,ahat2,w); magHhat2 = abs(Hhat2);
 
%Comparison of Magnitude Plots
Hf_1 = figure("paperunits", "inches", "paperposition", [0,0,6,4]);
subplot(2,2,1); plot(w/pi, magH, "g"); axis([0,1,0,0.7]);
xlabel("Digital Frequency in \pi units");
ylabel("Magnitude Response");
 
subplot(2,2,2); plot(w/pi, magHhat, "r"); axis([0,1,0,0.7]);
xlabel("Digital Frequency in \pi units");
ylabel("Magnitude Response");
 
subplot(2,2,3); plot(w/pi, magHhat1, "r"); axis([0,1,0,0.7]);
xlabel("Digital Frequency in \pi units");
ylabel("Magnitude Response");
 
subplot(2,2,4); plot(w/pi, magHhat2, "g"); axis([0,1,0,0.7]);
xlabel("Digital Frequency in \pi units");
ylabel("Magnitude Response");